We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that certain overrelaxation parameters form a divergent series. We combine our methods with a very general class of deterministic control sequences where, roughly speaking, we require that sooner or later we encounter a violated constraint if one exists. This requirement is satisfied, in particular, by the cyclic, repetitive and remotest set controls. Moreover, it is almost surely satisfied for random controls.

中文翻译：

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求解凸可行性问题的有限收敛的确定性和随机迭代方法

我们提出了一种有限收敛的方法来解决在无限可能的约束条件下定义的凸可行性问题。在该领域的其他工作之后，我们假定解集的内部是非空的，并且某些过松弛参数形成了一个发散级数。我们将我们的方法与一类非常通用的确定性控制序列结合在一起，大致来说，我们要求我们早晚遇到一个违反的约束（如果存在）。尤其是通过循环的，重复的和最远的设置控件可以满足此要求。而且，对于随机控制几乎可以肯定地满足了。